Inclusion Criteria:

          -  STEP 0: REGISTRATION ELIGIBILITY CRITERIA

          -  Patient must have had a radical prostatectomy (RP) as definitive therapy for
             histopathologically-proven prostatic adenocarcinoma

          -  Patient must have biochemical recurrence (BCR) after RP, with rising PSA defined as
             follows:

               -  If time to biochemical recurrence, (defined as time to first detectable PSA after
                  RP) is < 12 months, a minimum PSA level of >= 0.2 ng/mL and a confirmatory
                  reading of >= 0.2 ng/mL is required, per the American Urological Association
                  (AUA) definition (this includes patients with a persistent PSA reading of at
                  least 0.2 ng/mL)

               -  If time to biochemical recurrence, (defined as time to first detectable PSA after
                  RP) is >= 12 months, a minimum absolute PSA of 0.5 ng/mL is required

                    -  NOTE: Qualifying PSA values per above must be collected at least 4 weeks
                       after RP, with confirmatory persistent or elevated PSA collected at any
                       subsequent time point

          -  Patient must be negative or equivocal for extrapelvic metastatic disease by
             conventional imaging modalities (CIM) (i.e., bone scans, pelvic CT, or pelvic MRI),
             which must be done within 10-12 weeks prior to registration. Extra-pelvic metastases
             is defined as any osseous metastases and/or any extrapelvic soft tissue, lymph nodes
             and organ metastases; extra-pelvic is defined as superior to common iliac bifurcation,
             outside of standard prostate bed + whole pelvis nodal RT fields

          -  Baseline PET/CT scan (PET1) are eligible for this study if the SOC PET scan using
             18F-fluciclovine (Axumin) is completed during step 0 registration or up to 12 weeks
             prior to step 0 registration. The PET/CT scanners must meet scanner qualifications and
             scans must have an interpretation (or confirmation of an institutional clinical read)
             by a nuclear medicine physician or radiologist who has undergone 18F-fluciclovine
             (Axumin) reader training

          -  Patient must be a candidate for standard-of-care (SOC) post-prostatectomy radiation
             therapy (RT) to the prostate bed and pelvic nodes with androgen deprivation therapy
             (adjuvant)

          -  Patient must have the ability to provide written informed consent

          -  Patient must have an Eastern Cooperative Oncology Group (ECOG) performance status 0-2

          -  Patient must be able to lie flat and still for approximately 20-30 minutes or
             otherwise tolerate a PET/CT scan and radiation treatment planning and delivery

          -  Patient must be at a participating institution, which has agreed to perform the
             imaging research studies, completed the ECOG-American College of Radiology Imaging
             Network (ACRIN) defined PET/CT scanner qualification procedures and received
             ECOG-ACRIN PET/CT scanner approval

          -  Leukocytes >= 3,000/mcL (obtained within 4 weeks prior to registration)

          -  Absolute neutrophil count >= 1,500/mcL (obtained within 4 weeks prior to registration)

          -  Platelets >= 100,000/mcL (obtained within 4 weeks prior to registration)

          -  Total bilirubin =< institutional upper limit of normal (ULN) (obtained within 4 weeks
             prior to registration)

          -  Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase
             [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT])
             =< 2.5 x institutional ULN (obtained within 4 weeks prior to registration)

          -  Glomerular filtration rate (GFR) > 35 mL/min estimated by Cockcroft-Gault or measured
             directly by 24 hour urine creatinine (obtained within 4 weeks prior to registration)

          -  Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral
             therapy with undetectable viral load within 6 months are eligible for this trial

          -  For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral
             load must be undetectable on suppressive therapy, if indicated

          -  Patients with a history of hepatitis C virus (HCV) infection must have been treated
             and cured. For patients with HCV infection who are currently on treatment, they are
             eligible if they have an undetectable HCV viral load

          -  Patients with known history or current symptoms of cardiac disease, or history of
             treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac
             function using the New York Heart Association Functional Classification. To be
             eligible for this trial, patients should be class I or II (by patient symptoms) or A
             or B (by objective assessment)

          -  STEP 1: RANDOMIZATION ELIGIBILITY CRITERIA

          -  Patient must have completed a baseline SOC PET scan (PET1) with results of
             extra-pelvic metastases involvement known (positive or negative)

          -  For patients with negative extra-pelvic metastases, PET-imaging status of intra-pelvic
             nodes must be known (positive or negative)

          -  For patients with positive extra-pelvic metastases (defined as any PET positive
             lesions outside of standard salvage RT fields [prostate bed +/- typical whole
             pelvis]), the number of extra-pelvic lesions must be known (=< 5 or > 5 pelvic
             lesions)

        Exclusion Criteria:

          -  Patient must not have started androgen deprivation therapy for biochemical recurrence
             prior to baseline study PET/CT imaging

          -  Patient must not be enrolled in another therapeutic clinical trial

          -  Patient must not have any other malignancy within the last 2 years, other than
             superficial bladder cancer and skin basal cell carcinoma or cutaneous superficial
             squamous cell carcinoma that has not metastasized

          -  Patient must not have history of seizures or known condition that may cause
             predisposal to seizures (e.g., stroke or head trauma resulting in loss of
             consciousness) within 1 year of registration

          -  Patient must not have history of inflammatory bowel disease as this would increase
             risk of complication from radiotherapy or any gastrointestinal disorder affecting
             absorption

          -  Patient must not have had prior radiation therapy