Question

$Using \: binomial \: theorem \: proof \: that \: \\ {2}^{3n} - 7n - 1 \: is \: divisible \: by \: 49$

Answer 1

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Answer 2

((2)^3)^n -7n -1

= (8)^n -7n -1

= (1 +7)^n -7n -1

= nC0 + nC1(7) + nC2(7)^2...... + nCn(7)^n - 7n -1

= 1 + 7n + (7)^2 (nCo + nC1(7)..... nCn(7)^(n-2)) -7n - 1

= (7)^2 (nCo + nC1(7)..... nCn(7)^(n-2))

= 49 (nCo + nC1(7)..... nCn(7)^(n-2))

= 49m

So it is a multiple.