Yes, 3+7=10

Number Theory Level 2

If the least prime factor of positive integers a a and b b are 3 3 and 7 7 respectively, what must be a factor of ( a + b ) (a+b)~ ?

10 5 2 4

Manish Mayank by Manish Mayank , 20, India

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2 solutions

Calvin Tjahjadi
Oct 7, 2015

My thinking:

a = 3 × n u m b e r = o d d × n u m b e r = o d d a=3 \times number=odd \times number=odd

Likewise for b = 7 × n u m b e r b=7 \times number ; b would be an odd number since 7 - its least prime number - is an odd number.

( a + b ) = ( o d d + o d d ) = e v e n (a+b)=(odd+odd)=even

Since an even number should have 2 as their prime factor,

so, it would have been guaranteed that 2 is a factor of ( a + b ) (a+b)

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Avinash Kumar
Oct 6, 2015

lets take a as 9

b as 49

then a + b is 58

least prime factor is 2

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