Let a and b be positive integers such that ab+1

Jayson Hebert

Jayson Hebert

Answered question

2022-02-05

Let a and b be positive integers such that ab+1 divides a2+b2. Show that a2+b2ab+1 is the square of an integer. ?

Answer & Explanation

traciaul6y

traciaul6y

Beginner2022-02-06Added 14 answers

Step 1
Supposing that
a2+b2ab+1=k then
a2kba+b2k=0 solving for a
a=kb±k2b24(b2k)2
all the b's obeying b2=k and the a's obeying
a=kb are solutions. So
(bak111284327946416512525621636)
The question follows.

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