UKMT Special (Problem $10$ )

A sequence $a_1, a_2, a_3,...$ has $a_1 > 2$ and satisfies

$a_{n + 1} = \frac{a_n(a_n - 1)}{2}$

for all positive integers of $n$ .

For which values of $a_1$ are all the terms of the sequence odd integers?

[UKMT BMO $2020$ Round $2$ , Q $1$ ]

#Algebra

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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`	$\sum_{i=1}^3$
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Comments

You have until next Wednesday, $3:00$ 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 101010)

Comments

UKMT Special (Problem $10$ )