Question

if least prime factor of a is 3 and least prime factor of B is 7 what is the least prime factor of a + b

Answer 1

Solution=

Since 3 is least prime factor of a and 7 is least prime factor of b, hence none of them is divisible by 2 ( otherwise there least prime factor would have been 2 ).

Hence, we can conclude that bhot a and b are odd numbers.

a could be written as (2x+1)(2x+1) for x being any positive integer

Similarly b can be written as (2y+1)(2y+1) for y being any positive integer

a+b=2x+1+2y+1=2x+2y+2a+b=2x+1+2y+1=2x+2y+2

a+b=2(x+y+1)a+b=2(x+y+1)

So (a+b) is divisible by 2, also 2 is the smallest prime number.

Hence the least prime factor of (a+b) would be 2.

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Answer 2

The sum of a abd b is 10 Soleast prime factors are 2 &5