Mnemonic - Articles
Schumacher-Gauss, 30 June 1840

{.... A mental calculator called Dahse was here who, now and then, gave same notable proofs of his talents, but on the other hand, from time to time, made some remarkable errors, which fortunately didn't appear as often as the first. He was excellent in extracting the fifth (rational) root mentally, as he had noticed that the fifth power contains the same units as the root itself. I noticed that in our number system the (4n+1) th power contains the same units as the root itself, a theorem of which his was just a special case (for n=1). Is there an easy proof for this?

By the way, he doesn't understand a single thing about mathematics. PETERSEN has failed to teach him just a few elements. Now he has fallen into the hands of some non-comissioned officer of the Hamburg military, who travels around with him and lives from the tricks he does, even though I cannot understand why people are willing to pay money only to see him calculate mentally. If there are believable testamonials about the things he can do, then the exhibition will show nothing new. There is just a young man with a naive face who name the asked numbers after some period. ....}