Pick any two natural numbers m and n such that mn Now we def

Pick any two natural numbers m and n such that m>n. Now we define a=m^2n^2 and  b=2mn, then c=m^2+n^2. Now the three numbers a,b and c are Pythagorean triplets meaning a^2+b^2=c^2. Generate the Pythagorean triplet for the integers 5 and 7.

Solution

m=7 and n=5;
so a= 7²-5² = 49-25 = 24;
b=2mn = 2*5*7 = 70;
c= m² + n² = 7² + 5² = 49+25 = 74;

Since they are a Pythagorean triplet we can write that a²+b² = c² and see if it is correct;
24² + 70² = 74²
576+4900 = 5476
5476 = 5476;

Hence proved.