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Discounting one (Posted on 2018-01-10) Difficulty: 3 of 5
Any three of the integers {1, X, Y, Z} add up to a perfect square.

What are X, Y, & Z?

Hint: each is below 100.

No Solution Yet Submitted by Ady TZIDON    
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Interesting pattern (II) Comment 9 of 9 |
1+X+Y=(3m +2)^2
1+Y+Z=(4m +1)^2
1+Y+Z=(5m)^2
X+Y+Z=(5m +1)^2

X=10m +2
Y=9m^2+2m+1
Z=16m^2-2m-2

Table
m   1+X+Y   1+X+Z      1+Y+Z      X+Y+Z         X       Y       Z

0      2^2            1              0               1           2       1     -2
1      5^2           5^2          5^2         6^2         12    12     12
2      8^2           9^2         10^2       11^2        22     41     58    
3    11^2          13^2        15^2       16^2        32     88    136
4    14^2          17^2        20^2       21^2        42    153   246
...      ....              ....           ....           ....         ...      ...     ...

  Posted by armando on 2018-01-16 15:48:17
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