Fun pattern

Algebra Level 4

$3^2+4^2 = 5^2$

$10^2+11^2+12^2 = 13^2+14^2$

$21^2+22^2+23^2+24^2 = 25^2+26^2+27^2$

$36^2+37^2+38^2+39^2+40^2 = 41^2+42^2+43^2+44^2$ $\vdots$

$n^2+\cdots +6611^2+6612^2 = 6613^2+6615^2+\cdots + m^2$

What is the sum of $m$ and $n$ ?

2 solutions

Kamal Lohia
May 5, 2016

By finding pattern we can see that the last row is the 57th row. From there we can also find that n=6555 and m=6669.

Thanks for sharing your insight. Could you please elaborate more on how you found the pattern?

Pranshu Gaba - 5 years, 1 month ago

Owen Berendes
Mar 25, 2016

Not a solution, but the second term on the right side of the posted problem equation should be 6614^2 not 6615^2.