Question

what will be the remainder when (19^20-20^19) is divided by 7? ​

Answer 1

Given:

(19^20-20^19) is divided by 7

To find:

The remainder when (19^20-20^19) is divided by 7

Solution:

1) Remainder the number left when a number is divided with the other which means the number left after excluding the number which is exactly divisible by the given number.

2) By the remainder theorem if a number is completely divisible them the remainder is zero.

3) So the remainder is given by:

• $\frac{19^{20}-20^{19}}{7}$

• $\frac{(21-2)^{20}-(21-1)^{19}}{7}$

• $\frac{(-2)^{20}-(-1)^{19}}{7}$

• $\frac{(64)^{3}.2^{2}+1}{7}$

• $\frac{(63+1)^{3}.4+1}{7}$

• $\frac{(1)^{3}.4+1}{7}$

• $\frac{4+1}{7}$

• $\frac{5}{7}$

The numerator is smaller than the denominator then the remainder is 5

The remainder is 5