Menu Close

nice-calculus-number-theory-prove-thar-2-32-1-641-0-notice-without-calculator-and-only-with-the-u




Question Number 123287 by mnjuly1970 last updated on 24/Nov/20
                 ... nice  calculus ...         number theory            prove thar :::                                  2^(32) +1≡^(641) 0 ✓     notice: without calculator and only              with the use of congruence properties..
$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{nice}\:\:{calculus}\:… \\ $$$$\:\:\:\:\:\:\:{number}\:{theory} \\ $$$$\:\:\:\:\:\:\:\:\:\:{prove}\:{thar}\:::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}^{\mathrm{32}} +\mathrm{1}\overset{\mathrm{641}} {\equiv}\mathrm{0}\:\checkmark \\ $$$$\:\:\:{notice}:\:{without}\:{calculator}\:{and}\:{only} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{with}\:{the}\:{use}\:{of}\:{congruence}\:{properties}.. \\ $$
Answered by MJS_new last updated on 24/Nov/20
just divide?  I′ve been having problems with proofs that  are easy to calculate...  2^(32) +1=4 294 967 297=641×6700417  maybe try to show that 2^(100) +1≡0(401)?
$$\mathrm{just}\:\mathrm{divide}? \\ $$$$\mathrm{I}'\mathrm{ve}\:\mathrm{been}\:\mathrm{having}\:\mathrm{problems}\:\mathrm{with}\:\mathrm{proofs}\:\mathrm{that} \\ $$$$\mathrm{are}\:\mathrm{easy}\:\mathrm{to}\:\mathrm{calculate}… \\ $$$$\mathrm{2}^{\mathrm{32}} +\mathrm{1}=\mathrm{4}\:\mathrm{294}\:\mathrm{967}\:\mathrm{297}=\mathrm{641}×\mathrm{6700417} \\ $$$$\mathrm{maybe}\:\mathrm{try}\:\mathrm{to}\:\mathrm{show}\:\mathrm{that}\:\mathrm{2}^{\mathrm{100}} +\mathrm{1}\equiv\mathrm{0}\left(\mathrm{401}\right)? \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *