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Question Number 137364 by liberty last updated on 02/Apr/21
Findtheremainder730divideby10
Answered by MJS_new last updated on 02/Apr/21
70=171=772=4973=34374=240130=7×4+2⇒answeris9
Answered by EDWIN88 last updated on 02/Apr/21
wehave730=4915≡915(mod10)wecanapplyBinomialTheorem915=(10−1)15=∑15k=0(15k)1015−k.(−1)ksoclearly915≡−1(mod10)=9(mod10)thereforetheremainder730:10isequalto9.
Answered by benjo_mathlover last updated on 02/Apr/21
ByEulerphiTheorem7φ(n)=1(modn)wefindφ(10)=10(1−12)(1−15)=4so730=(74)7×72=1×72(mod10)=49(mod10)=9(mod10)itfollowsthattheremainderis9
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