+128406 Can anyone think of 5 positive integers, a,b,c,d and e such that
a^2 + b^2 + c^2 + d^2 = e^2 ?????
[ There is more than one correct answer ] !!!!!!
(Also....and I should have been more specific....the integers are all different ) !!!!
+128406 Ding!! Ding!! Ding!!!......we have a winner!!
kitty<3 !!!!
I came up with........
1 , 2 , 8, 10, 13
Note, that any positive integer multiples of these answers "work," too. (Just like in the Pythagorean "Multiples")
[Mmmm...I wonder if there is a general "formula" for generating the "correct" values??? ]
+33614 Here's a way of generating more sets of values:
Choose a Pythagorean triple, say 3, 4, 5. Let a = 3m, b = 4m, c = 3n, d = 4n, and e = 5√(m2 + n2)
a2 + b2 + c2 + d2 = (32 + 42)m2 + (32 + 42)n2 = (32 + 42)(m2 + n2) = 52(m2 + n2) = e2
Now choose m and n to be part of another Pythagorean triple, say m = 5 and n = 12, and we have e as an integer (=5*13).
So a = 3*5 = 15; b = 4*5 = 20; c = 3*12 = 36; d = 4*12 = 48; e = 5*13 = 65;
$${{\mathtt{15}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{20}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{36}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{48}}}^{{\mathtt{2}}} = {\mathtt{4\,225}}$$
$${{\mathtt{65}}}^{{\mathtt{2}}} = {\mathtt{4\,225}}$$
(I don't remember seeing Chris's last line when I gave my previous answer. Hmm!)
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