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CAT 2002 — QA Question 11

Remainder of a to the power n, divided by b.Easy

For all integers n > 0, 76n – 66n is divisible by

Answer & solution

  • A

    13

  • B

    127

  • C

    559

  • All of these

Solution

Given, 76n – 66n = 72×3n – 6​​​​​​​2×3n = (73n)2 – (6​​​​​​3n)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).

CAT 2002 QA Q11: For all integers n > 0, 7 6n – 6 6n is divisible by — Solution | TheCATExam