A student claims that \(20^2 + 21^2 = 29^2\), then the equation \(20^3 + 21^3 = 29^3\) must also be true. Is the student correct? Justify.
Answer:
Evaluating first equation: \(LHS = 20^2 + 21^2 =\)
\(RHS = 29^2 =\)
Since , the equation \(20^2 + 21^2 = 29^2\) is .
Evaluating the second equation: \(LHS = 20^3 + 21^3 =\)
\(RHS = 29^3 =\)
Since , the equation \(20^3 + 21^3 = 29^3\) is . This is with Fermat’s Last Theorem.
Therefore, the student's assumption is .