A number theory problem by Soumava Pal

Number Theory Level 4

We have two positive integers a a and b b such that a ÷ b = b . a a \div b=b.a

Note that a . b a.b refers to the decimal expression, where if a = 93 , b = 28 a=93, b=28 then a . b = 93.28 a.b=93.28 .

Find the remainder when 1000000007 is divided by a + b a+b .

2 29 31 6

Soumava Pal by Soumava Pal , 22, India

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1 solution

Soumava Pal
Feb 4, 2016

I found it pretty remarkable to see that 5/2=2.5 happened only for 2 and 5. As I went on trying for bigger numbers I was surprised to see that no number satisfied this strange property. In fact I think (2,5) is the only solution to this expression.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Very good observation

soura gd - 5 years, 4 months ago

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I have a strange feeling that i know you. :P thanks.

Soumava Pal - 5 years, 4 months ago

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You know me indeed. B)

soura gd - 5 years, 4 months ago

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