UKMT Special (Problem $8$ )

It is well known that, for each positive integer $n$ :

$1^3 + 2^3 + ... + n^3 = \frac{n^2(n + 1)^2}{4}$

and so is a square. Determine whether or not there is a positive integer $m$ such that

$(m + 1)^3 + (m + 2)^3 + ... + (2m)^3$

is a square.

[UKMT BMO $2018$ Round $2$ , Q $3$ ]

#Algebra

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Comments

You have until $1^{st}$ December, $3:00$ pm!

Yajat Shamji - 7 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

UKMT Special (Problem 888)

Comments

UKMT Special (Problem $8$ )