What would be the least total no. which give the remainder 1,2 and 3 when divided by 7,9 and 11?
1,2 and 3 when divided by 7,9 and 11?
hence
x= 1 mod 7
x= 2 mod 9
x =3 mod 11
now 7 ,9 and 11 are pair wise coprime
x = 1 a1b1 + 2 a2b2 + 3 a3b3 mod 7*9*11(or 693)
where a1 = 9*11 = 99
a2 = 7 * 11 = 77
a3 = 7 * 9 = 63
and
a1b1 = 1 mod 7
a2b2 = 1 mod 9
a3b3 = 1 mod 11
a1 = 99 so b1 = 99 mod 7 or 1 mod 7 so b1 = 1
77b2 mod 9 = 1 so 5b2 mod 9 = 1 so b2= 2 (as 5*2 = 10 mod 9)
63b3 = 1 mod 11 or 8b3 =1 mod 11 so b3 = 7 as 7 * 8 = 56 = 1 mod 11
So x = 1 * 99 * 1 + 2 * 77 * 2 + 3 * 63 * 7 mod 693 = 1730 mod 693
= 344 mod 693
So x if of the form 693n + 344 or lowest x = 344
