tmua.fyi Paper 2 Challenge 2 · Question 5

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tmua.fyi Paper 2 Challenge 2 · Q5

Paper 2Logic & proof

The numbers $1,2,3,\ldots,2026$ are written on a board. Repeatedly, two of the numbers, $a$ and $b$ , are rubbed out and $|a-b|$ is written in their place. After $2025$ such steps a single number is left. Which of the following must be true of it?

AIt is

0

BIt is

1

CIt is odd.

DIt is even.

EIt is a multiple of

1013

FIt is at least

1013

GIt is prime.

HNone of these must be true.

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