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Show that 2^4n – 2^n (7n+1) is some multiple of the squre of 14. where n is positive integer.

Show that 2^4n – 2^n (7n+1) is some multiple of the squre of 14. where n is positive integer.

Grade:11

1 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
4 years ago
=2^n(2^3n-7n-1)

=2^n{8^n-1–7n}

=2^n{(7+1)^n-1–7n}

=2^n{(multiples of 7 and+1)-1–7n}

=2^n{multiples of 7 -7n}

It is multiple of 14 for all values of n

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