Fermat's Last theorems! can you show that the negative real exponent solutions are in one-to-one correspondenc?
Show that the solutions of Fermat's last theorem for negative real exponent "-n" are in one-to-one correspondence with solutions for positive n.
Fermat's Last Theorem states that "(x^n)+(y^n)=(z^n)" has no integer solutions for n>2 and x,y,z≠0.
- 9 years ago
Begin by putting it into an equation form:
Multiply both sides by (x^n)(y^n)(z^n)
Now use one of the exponent rules (a^n)(b^n)=(ab)^n to get:
Substitute in yz=a,xz=b,xy=c:
As a,b,c are integers as they are the product of two integers we have shown that they are inn one-to-one correspondance.Source(s): Maths A-Level