Math, asked by sushantha6235, 8 months ago

For two positive integers 158 and 37, find out whether there
exist any two unique integers which satisfy the Euclid's
division lemma

Answers

Answered by pallelapavankalyan
1

Step-by-step explanation:

r must satisfy0≤r<b

Proof,

..,a−3b,a−2b,a−b,a,a+b,a+2b,a+3b,..

clearly it is an arithmetic progression with common difference b and it extends infinitely in both directions.

Let r be the smallest non-negative term of this arithmetic progression.Then,there exists a non-negative integer q such that,

a−bq=r

=>a=bq+r

As,r is the smallest non-negative integer satisfying the result.Therefore, 0≤r≤b

Thus, we have

a=bq

1

+r

1

, 0≤r

1

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