六年级奥数课堂：数论的方法技巧之二
六年级奥数课堂：数论的方法技巧之二
1
2
3
100a+10b+c=10a+b+10b+c+10a+c 80a=b+ca≥1b≤9c≤9
2 17
d+ab+c≤9abcd13
4k+112+21506+605
3 1枚11枚11枚51枚54枚11枚13枚11枚11枚51110
1枚1111 0+1=111QQ
1枚1Q11枚11枚5Q1枚54枚1Q41枚1Q2QQ
11 10P枚1P+101112P+10
43×3939
9100313931993
9
5 99999999
99999999999998
9999=9998-98+9998-96+…+
=9998-2+9998+9998+2+…+
=9998+96+9998+98
9999999999
6 123999999
23303130301322=1024999
30
2612×613603×604594×59
303330×33313231×32
31×32=9923030
81+2+…+100
7 123999999899999999999999
010000999999919999998499999950000009×7=63500000063×5000000=315000000
8 999900019999 0734 0+7=3+4101
9999nm=9999-n9999m≠n
m+n=9999999999999999
9999=99×101101
m89
1+2+3+…+n
2m×88=89×kk
8989 8889|m
1×88×2×87×3×86×…×44×45=88
m×88=89×kk=n×q
89898889|m
5
S2S4S=35
11 1×2×3×…×n106n
n1×2×…×nnnn
1×2×3×…×400580+16+3=9925n=4001×2×…×n99 742525
n=4301×2×…×n106
n=4351×2×…×n107
n434