Discussion

Question:

What is the remainder if 19²⁰ – 20¹⁹ is divided by 7?

Explanation:

$R [\frac{19^{20}}{7}]$ = $R [\frac{5^{20}}{7}]$ = $R [\frac{25^{10}}{7}]$ = $R [\frac{4^{10}}{7}]$ = $R [\frac{16^{5}}{7}]$ = $R [\frac{2^{5}}{7}]$ = $R [\frac{32}{7}]$ = 4

$R [\frac{20^{19}}{7}]$ = $R [\frac{{(- 1)}^{19}}{7}]$ = -1

$R [\frac{19^{20} - 20^{19}}{7}]$ = 4 - (-1) = 5

Hence, option (a).

» Your doubt will be displayed only after approval.

Doubts

Feedback