Having Fun With 69

Number Theory Level 2

a 2 − b 2 = 69 a^{2} - b^{2} = 69

How many positive integer pair(s) of ( a , b ) (a,b) for a > b a > b that satisfy the equation above?

2 0 4 1 3

Muhammad Rizki Fadillah by Muhammad Rizki Fadillah , 31, Indonesia

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1 solution

Muhammad Ardivan
Jul 8, 2015

(a+b)(a-b)= 69

Case 1, (a+b)(a-b)=69*1

From that we get a=35 and b=34 (since a>b)

Case 2, (a+b)(a-b)=23*3

And we get a=13 and b =10

So there is 2 pairs of them , that satisfy the question above

1 Helpful 0 Interesting 0 Brilliant 0 Confused

good job, thank you.

Muhammad Rizki Fadillah - 5 years, 11 months ago

The Title of the question is awesome xD

Kushagra Sahni - 5 years, 11 months ago

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