TMUA-P2-PRF2-016 — Paper P2 · Proof by cases · Level 3

Options

1. A
   Write $n=2k+1$ so $n^2-1=4k(k+1)$; this is divisible by $4$, so done.
2. B
   Check $n=1$ only.
3. C
   Odd squares are $1$ modulo $4$, so done.
4. D
   Write $n=2k+1$ so $n^2-1=4k(k+1)$; since one of $k,k+1$ is even, $k(k+1)$ is even, so $4$ times an even number is divisible by $8$. Cases $k$ even and $k$ odd both work.

Letters only — the answer key is hidden. Work it out, then check the solution below.

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