MathDB

Let

N

be a positive integer such that the sum of the squares of all positive divisors of

N

is equal to the product

N(N+3)

. Prove that there exist two indices

i

and

j

such that

N=F_iF_j

where

(F_i)_{n=1}^{\infty}

is the Fibonacci sequence defined as

F_1=F_2=1

and

F_n=F_{n-1}+F_{n-2}

for

n\geq 3

.
Proposed by Alain Rossier, Switzerland

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