perplexus.info :: Just Math : 2 equal sums

2 equal sums (Posted on 2016-04-11)

What is the largest n for which
1^2+2^2+3^2+ ... +n^2 = 1+2+3+ ... +m has a solution
with integer values of n & m?.

No Solution Yet Submitted by Ady TZIDON

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re: computer exploration -- possible spoiler

| Comment 2 of 3 |

UBASIC, with extended precision has verified 85 as the highest n under 10 million that satisfies the criterion.

10 sqs = 0

20 For n = 1 To 9999999

30 sqs = sqs + n * n

40 mp = Sqr(sqs * 2)

50 m = Int(mp)

60 If m * (m + 1) / 2 = sqs Then

70 :print n , Str(m) , " " , Str(sqs)

80 Next

Posted by Charlie on 2016-04-11 22:44:38

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