Question

URGENT PLEASE HELP ASAP

Let a≡ (3∧-1+5^-1+7∧-1)^-1 (mod 11). What is the remainder when a is divided by 11?

Answer 1

If you write the given equation in fraction form, it would be presented this way:


`(1)/( (1)/(3) + (1)/(5)+ (1)/(7) )`

The exponent, ⁻¹, stands for inverse or reciprocal. Let's simplify this fraction first before dividing it by 11. Starting from the denominator, find the greatest common factor of 3, 5 and 7. That would be 3×5×7 = 105. Divide 105 to 3, 5 and 7, respectively, and add to their numerators. That would be


`(1)/( (36+22+16)/(105) ) = 105/71`

Now, we divide this by 11 and the answer is 0.13444. That means the remainder is 13444/10.