Step by step
The question
Question: is 50 ≡ 21 (mod 4)?
50 ≡ 21 (mod 4) ?
This sign means: they leave the same remainder when we divide by 4.
We say congruent.
≡ (mod n): the same remainder after ÷ n
1 Each remainder
Divide 50 by 4: 4 goes 12 times, that is 48, and 2 is left over.
50 = 4 × 12 + 2
21 is 4 × 5, plus 1.
21 = 4 × 5 + 1
Careful!
50 and 21 are different numbers.
The question is only about their remainders.
Careful: compare the remainders, not the numbers
2 Compare the remainders
2 and 1: different remainders.
= 2 ≠ 1
So no, they are not congruent mod 4.
= no: different remainders mod 4
3 Check
Another way: the difference 29 is not a multiple of 4.
Right!
50 − 21 = 29, not a multiple of 4
Let's look back.
First: each remainder.
Then: compare the remainders.
Last: check.
Answer
= no: different remainders mod 4