Necklaces, Periodic Points and Permutation Representations

Somnath Basu, Anindita Bose, Sumit Sinha and Pankaj Vishe

The authors are second year students of BMath Hons in the Indian Statistical Institute, Bangalore.

One of the most ubiquitous results of elementary number theory is the so-called Fermat's little theorem. Pierre de Fermat was an amateur mathematician to whom are credited several deep and stunning results in mathematics. Let us list a few. He proved the impossibility of solving in non-zero integers the equation X^4 + Y^4 = Z^2 and, in the process, discovered the now-famous method of descent. He proved that a prime of the form 4n+1 is a sum of two squares of integers. He is also credited, along with Newton and Leibniz, with the discovery of the integral calculus

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Address for Correspondence
Somnath Basu, Anindita Bose Sumit Sinha and Pankaj Vishe Indian Statistical Institute 
8th Mile Mysore Road 
Bangalore 560 059, India.