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Sum of 4 squares (Posted on 2018-07-08) Difficulty: 3 of 5
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.

See The Solution Submitted by Ady TZIDON    
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solution | Comment 3 of 4 |
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 2018-07-08 20:15:11
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