a congruent to b modulo n
a is congruent to b iff a and b are natural numbers that have the same remainder when divided by n.
When we say that a is congruent to b modulo n, we mean that a and b give the same remainder when divided by n. In other words, the difference between a and b is divisible by n.
In mathematical notation, we can write it as follows:
a ≡ b (mod n)
This is read as a is congruent to b modulo n.
For example, we can say that 13 is congruent to 1 modulo 6, because:
13 ≡ 1 (mod 6)
This is true because when we divide 13 by 6, we get a remainder of 1:
13 ÷ 6 = 2 remainder 1
Similarly, when we divide 1 by 6, we also get a remainder of 1:
1 ÷ 6 = 0 remainder 1
Therefore, 13 and 1 are equivalent modulo 6, and we can say that 13 is congruent to 1 modulo 6.
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