How many integral solutions are there?

Number Theory Level 2

6 x + 15 y = 2 20 \large 6x + 15y = 2^{20}

If the equation above has A A integral solutions. Input your answer as 2020 A 2020 A .


The answer is 0.

Barry Leung by Barry Leung , 17, Hong Kong

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1 solution

The given equation is equivalent to 3 ( 2 x + 5 y ) = 2 20 3(2x+5y)=2^{20}

Since the R.H.S. doesn't have 3 3 as a factor, the answer is 0 \boxed 0 .

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