Parity from division

Algebra Level pending

Given positive real numbers a , b a, b so that these two below are satisfied: a 2 + 1 ⋮ b + 1 b 2 + 1 ⋮ a + 1 a^2+1\vdots b+1\\b^2+1\vdots a+1

What is the parity of a a and b b ?

a a is odd, b b is even There are no solutions. Both are even Both are odd b b is odd, a a is even

Tin Le by Tin Le , 15, Vietnam

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