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n positive integer and d_{k}, k<=n its divisors

Source: bmo 1989

April 23, 2007

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Problem Statement

Let

n

be a positive integer and let

d_{1},d_{2},,\ldots ,d_{k}

be its divisors, such that

1=d_{1}<d_{2}<\ldots <d_{k}=n

. Find all values of

n

for which

k\geq 4

and

n=d_{1}^{2}+d_{2}^{2}+d_{3}^{2}+d_{4}^{2}

.

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