Fundamental of Mathematics 1

Number Theory Level 2

Find number of pairs of positive integers ( m , n ) (m,n) satisfying m 2 − n 2 = 28 m^2-n^2=28 .

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Vedant Sharda by Vedant Sharda , 20, India

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1 solution

Vedant Sharda
Jan 10, 2016

m²-n²=28

(m-n)(m+n)=28

28=1×28, 2×14, 4×7

Put (m-n)=1 & (m+n)=28

But from this m&n are not natural

Similarly put another values of (m-n) & (m+n)

So only 1 value of m&n satisfy this i.e m=8 & n=6

Only 1 pair (8,6)

4 Helpful 0 Interesting 0 Brilliant 0 Confused

We can note that(without substitution) that both factors must either be both odd or both even simultaneously. Then only choice is 2×14 and the answer follows

Anand Chitrao - 5 years, 5 months ago

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