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Part of 1989 Balkan MO

Problems(1)

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

Source: bmo 1989

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

k\geq 4

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

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