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Consider a linear congruence a ≡ b (mod m), Choose the false relation from the option given below:

Consider a linear congruence a ≡ b (mod m), Choose the false relation from the option given below: Correct Answer a =<span id="docs-internal-guid-c67c4fda-7fff-ca25-20db-f0e73c813045"><span style=" background-color: transparent; font-variant-numeric: normal; font-variant-east-asian: normal; vertical-align: baseline; white-space: pre-wrap;"> Kb + m</span></span>

Concept:

  • If a and b are integers and n > 0, we write a ≡ b (mod m).
  • We read this as “a is congruent to b modulo m". 
  • We can write this congruency only if the remainder of a and b, when divided by m is the same.
  • We can define modulo in another way, if a - b is completely divisible by m, then m will be modulo of a and b.


In general, we can write the above statement as,

a = Km + b where k is any positive integer.

Explanation:

From the above discussion, we can conclude that,

except the relation a = kb + m, all other are correct.

Hence, option 1 will be the correct answer.

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