Question

State the Euclid's division lemma for teo positive integers a and b

Answer 1

$\huge\underline\bold\red{Answer :-}$

• If 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=bq1+r1,   
• 0≤r1≤b

Answer 2

Answer:

install na only 21 MB yaar please

I am waiting for u