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He worked on a wide variety of different topics. His work on differential geometry and contributions to Fermat's Last Theorem are important. Here he proved the theorem for n=7 in 1839. In number theory he showed that the number of divisions in the Euclidean algorithm never exceeds five times the number of digits in the smaller number.
On the applied side he worked on engineering mathematics and elasticity where two elastic constants are named after him. He studied diffusion in crystalline material.
References elsewhere in this archive:
Tell me about Lamé's work on Fermat's last theorem
Lamé worked on the Ellipse, on the Hyperbola and on the Lamé Curves
References:
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