find all numbers a is greater than or equal to 20 so that 6a

find all numbers a is greater than or equal to 20 so that 6a is congruent with 16 (mod 20)

Solution

I As per the definition 6a is congruent with 16(mod20)means the difference between 6a & 16 should be a multiple of 20.In other words, (6a-16) should be divisible by 20 without any remainder. The condition in the problem is that a must be equal or greater than 20.The logic is that only those numbers ending in zero will be divisible by 20.Therefore,(6a-16) should be such that it should always result in to a number ending in zero. This is possible only a=6,16,26,36etc.Since a should be greater or equal to 20, the answers are 26,36,46,56,66,etc.