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Sum of 2 divisors of n^2+1/2

Source: 2014 China TST 3 Day 2 Q4

April 5, 2014
number theory proposednumber theoryVieta Jumping

Problem Statement

Let kk be a fixed odd integer, k>3k>3. Prove: There exist infinitely many positive integers nn, such that there are two positive integers d1,d2d_1, d_2 satisfying d1,d2d_1,d_2 each dividing n2+12\frac{n^2+1}{2}, and d1+d2=n+kd_1+d_2=n+k.
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