Question

The remainder when 98 is divided by 101 is equal to

Answer 1

could go in decimals man....

Answer 2

Answer:

50

Step-by-step explanation:

Using Wilson’s Theorem  which states that

(−1)!≡−1mod

(p−1)!≡−1modp for prime. 101 just so happens to be prime; thus,

100!=100×99×98!≡−1mod101

Now, what to do about that pesky 100∗99

100 ≡−1mod101

99   ≡−2mod101

Multiplying the two gives

100×99 ≡ 2mod101

And, substituting back into our Wilson’s theorem relation, we have

2∗98!≡−1mod101

One more step: replace −1

with its positive value 100=101−1

2∗98!≡100mod101

Divide by 2, and we have

98!  ≡  50mod101

Hence the answer is 50