If $$77^{77}+77$$​ is divided by 78, then the remainder will be:

Correct option is A

Given:

Divisor = 78

Dividend = $$(77)^{77}+77$$​​

Formula Used:

When $$(a^x+b^x)=(a+b).....$$, where x is an odd number.

Solution:

We can write, $$(77)^{77}+77=[77^{77}+1]+76$$​​

By dividing both the terms by 78, we get

​$$=\frac{77^{77}+1}{78}+\frac{76}{78}$$​​

​$$=\frac{77^{77}+1^{77}}{78}+\frac{76}{78}$$ 

= 0 + 76 

As per the formula, the first term will be clearly divisible by 78, so we get,

Remainder = 76