For all integers n > 0, 76n – 66n is divisible by
Explanation:
Given, 76n – 66n = 72×3n – 62×3n = (73n)2 – (63n)2
Factorizing the given expression,
(73n – 63n)(73n + 63n)
i.e. (7n – 6n)(72n + 62n + 7n6n)(73n + 63n) ... (i)
Substitute n = 1 in equation (i),
The three factors are 1, 127 and 559.
Since 559 is divisible by 13, hence 13 will also be a factor.
Hence, option (d).
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