engleski

Two divisors of (n^2+1)/2 summing up to δn+ε, for δ and ε even

We deal with the problem of the existence of two divisors of (n^2+1)/2 whose sum is equal to δn+ε, in the case when δ and ε are even, or more precisely in the case in which  δ = ε+2 = 0 or 2 (mod 4). We will completely solve the cases δ = 2, δ = 4 and ε = 0. In our proofs we use Diophantine equations and their properties, with a special accent on Pellian equations and their properties.

sum of divisors; continued fractions; Pell's equations

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