Question

Prove that if a and b are integers with b > 0, then there exist unique integers q
and r satisfying a = qb + r, where 5b <r < 6b​

Answer 1

Answer:

Euclid’s  division  Lemma:

It tells us about the divisibility of integers. It states that any positive integer ‘a’ can be divided by any other positive integer ‘ b’ in such a way that it leaves a remainder ‘r’.

Euclid's division Lemma states that for any two positive  integers  ‘a’  and  ‘b’  there  exist two  unique  whole  numbers  ‘q’  and ‘r’  such that , a = bq  +  r, where 0≤r<b.

Here, a= Dividend, b= Divisor, q= quotient and r = Remainder.

Hence, the values 'r’ can take  0≤r<b.