Can you find
four numbers such that the sum of every two and the sum of all four may be
perfect squares?
Answer: Besides
several other answers, the smallest number that satisfies the conditions are:
a= 10430, b= 3970, c= 2114, d=386
a+b = 10430 +3970 = 14400 =120²
a+c = 10430 +2114 = 12544 = 112²
a+d = 10430 + 386 = 10816 -104²
b+c = 3970 +2114 = 6084 =78²
b+d = 3970 +386 = 4356 = 66²
c +d = 2114 +386 =2500 =50²
a+b+c+d = 10430 + 3970 + 2114 + 386 =16900
=130²
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