Mathematicians Of The Day

30th June

On this day in 1742, Leonard Euler claimed in a letter to Goldbach that prime numbers of the form 4n+ 1 are represented uniquely as a sum of two squares.
He also mentioned that 641 divides 232+12^{32} + 1, thereby disproving Fermat's claim that all the so-called numbers Fermat numbers Fn=22n+1F_n = 2^{2^n} + 1 are prime. Years later we have not found another with n > 4 which is prime.

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Quotation of the day

From John William Strutt
Examples ... which might be multiplied ad libitum, show how difficult it often is for an experimenter to interpret his results without the aid of mathematics.
Quoted in E T Bell Men of Mathematics