Question

find the smallest value of a if 10a +5 is divisible by three​

Answer 1

If a is a positive whole number, ans is 1.
If a is any positive number, ans is 1/10.


Hope this helps.

Answer 2

Answer:

If a is negative then the smallest value of a that divides 10a + 5 by 3 is

-(3n + 2)/10. Confirming by induction method.

if n = 1, a = -(3*1 + 2)/10 => -5/10

therefore, 10a + 5 = 0 which is divisible by 3.

if n = -1, a = -(3n+2)/10 = 1/10

therefore (1/10)*10 + 5 => 6 which is divisible by 3.

.....

likewise the smallest value of a that divides 10a + 5 by 3 is -(3n+2)/10 where n is -ve infinity.