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