Question

for every pair of positive integers a and b there exist a unique pair of whole number q and r such that a=bq+r give examples of a and b whereever possible satisfying a) r=0 b) q=0 c) r>b d) if a< b what can be said about q and r

Answer 1

a) for r=0 ,a= bq
q =0,1,2,3,...etc.
so a=0, b,2b, 3b, ...etc
b) if q=0, then a=r
r=0,1,2,3,...etc
so a= 0,1,2,3,4,..etc.
c)r>b
so r can be b+1, b+2, b+3, b+4,.....etc
a= qb+ b+1
or a=qb+b+2
or a=qb +b+3.
.....etc.
d)if a<b, then q should be equal to zero.because if q becomes more than zero , then a will not be less than zero.
and r should be less than b , so that a donot become equal to or greater than b.