Number of ordered pairs

Number Theory Level 3

Find the number of ordered pairs of whole numbers $(x,y)$ such that $(xy-7)^2 = x^2 +y^2$ .

1 solution

Zerocool 141
Jan 20, 2017

@Pi Han Goh Sir what is ur method ? did u count the ordered pairs?

Instead of asking me how I solved it, it would be helpful for you to explain where you're stuck on.

I'm not here to give you all the answers. This is not a "help me with my homework" site.

Pi Han Goh - 4 years, 4 months ago

i could only count two pairs (3,4) and (4,3) i tried to proceed with taking x=cosx and y=sinx .but nothing worked out .

Zerocool 141 - 4 years, 4 months ago

Trigo approach never works for a "count number of integer solutions".

Hint: Start with "What is the parity of x and y?" That is, should x and y be odd? Or can they both be even? Or can they be one odd and one even?"

Pi Han Goh - 4 years, 4 months ago

@Pi Han Goh – i have got the answer sir .thank u .

Zerocool 141 - 4 years, 4 months ago