### Allan Joseph Champneys Cunningham

*Based on the obituary by A.E. Western, J. London Math. Soc. (1928) 317-318*

Allan Cunningham was born in 1842 in Delhi. His early career, after military training in London, was with the East India Company's Bengal (later Royal) Engineers. He was Instructor in Mathematics at the Thomason Civil Engineering College, Roorkee, from 1871-1881. After returning to England in 1881, he held various teaching appointments at army establishments in Chatham, Dublin and Shorncliffe. He retired from the Army in 1891.

The remainder of his life was devoted to the Theory of Numbers, his interests being confined to Fermat's theorem, residues of powers, quadratic and higher reciprocity and quadratic forms. He applied his studies in these areas to factorising numbers of the form a^{n} ± b^{n}. This included Mersenne numbers 2^{p}-1 and Fermat numbers 2^{2n}+1 and he was able to find new factors. He was a skilled computationalist and produced copious tables in this area. Some of these tables include:

*Binary Canon*: This gives corresponding values of *x* and *r* in the congruence 2^{x} r (mod p);
*Quadratic partitions*: This gives values of *x* and *y* satisfying x^{2}+dy^{2}=p, for various values of d;
*Haupt-exponents, residue-indices, etc.* (jointly with H.J. Woodall and T.G. Creak): This gives values of *n* for given *y* in y^{n} 1 (mod p);
*Fundamental congruence solutions* (jointly with T.G. Creak): This gives a value of *y* for given *n* in the above congruence;
*Binomial factorisations*: This give all the roots of the above congruence for given *n* and many other tables relating to factors of numbers of certain forms.

Cunningham died in London in 1928 at the age of 86. He left a legacy to improve methods of factorising large integers. This legacy was later taken up by A.E. Western, whose *Table of Indices and Primitive Roots* was written with J.C.P. Miller.

Cunningham's name lives on in the Cunningham Project.
For a list of Cunningham's publications, see The Jahrbuch Project.

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Last updated at 26th February 2003