The number N is a sum of 4 different numbers, each being a square of one of the 4 smallest divisors of N (e.g. N=36 does not qualify since 1^2+2^2+3^2+4^2
sums up to 30, not 36.)
Provide a full list of
similar numbers or show that none exist.
Thanks to Steven Lord for clearing away most of the brush.
We have N = 5 + a^2 + b^2 with N even. Since (a,b) have different parity, N is not divisible by 4.
So N = 2pq with p and q odd where p = the smallest factor > 2 of N. The next smallest factor must then be 2p which gives N = 2pq = 5(1 + p^2).
If 5 doesn't factor p then p = 3 giving the impossibility 6q = 50.
If 5 factors p then p = 5 and we get the solution Charlie found.

Posted by xdog
on 20180708 20:15:11 