Mathematics
Senior High
赤矢印の変形がわかりません
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第3問 (1) N = 10° × α+10" xaz+10°× as +10×α
+ 104 × as +10°×α + 102×
=10° (10²×α+10×az+α3) +103 (102×a4 +10×
+10² x
=10" x AL+1013×A2+ A3
10°=1000=7×ウエオ143-1 であるから
N=(10²)2×A1 +10°×A2+A3
=(7×143-1)× A + (7×143-1 ) ×A2+A3
A
[
=7B+A1-A2+ A (Bは整数)
7B は 7の倍数であるから,Nを7で割ったときの余りと
割ったときの余りは常に一致する。(カ②)
N=473586129 のとき, A1 = 473, A2=586, As = 129 で
1 ± 1 -16
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