Prove that $(2n-1)(3^n)+1 ≡ 0 \pmod 4$.
2026-04-05 01:09:14.1775351354
Prove that $(2n-1)(3^n)+1$ is always divisible by 4.
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HINT: $3 \equiv -1 \pmod 4$. Hence when $n$ is odd $3^n \equiv -1 \pmod 4$, while $3^n \equiv 1 \pmod 4$ when $n$ is even. Now cosider the two cases of $n$ even and $n$ odd.