Question -
Answer -
Given:
23n –7n – 1
So, 23n –7n – 1 = 8n – 7n – 1
Now,
8n –7n – 1
8n =7n + 1
= (1 + 7) n
= nC0 + nC1 (7)1 + nC2 (7)2 + nC3 (7)3 + nC4 (7)2 + nC5 (7)1 +… + nCn (7) n
8n = 1+ 7n + 49 [nC2 + nC3 (71)+ nC4 (72) + … + nCn (7) n-2]
8n – 1– 7n = 49 (integer)
So now,
8n – 1– 7n is divisible by 49
Or
23n –1 – 7n is divisible by 49.
Hence proved.