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六年级奥数课堂：数论的方法技巧之一 1abb0qr a=bq+r0≤rb qr r=0a=bqabb|abaab 2a|cb|cabab|c 31n p1p2pka1a2ak1n 4n1 dn=a1+1a2+1ak+1 5nn+1xyx≤y-1 1n=an10n+an-110n-1+…+a0 2a=bq+r 42n=2mtt 1 20232023983 a3a2a1a0 2023a3+100a2+10a1+a0 10 10a3+a2+a1+a0=10a3+10a2+10a1+10a0 10 990a3+90a2-9a0=2023 110a3+10a2-a0=222 a0=8a2=1a3=2 218 a+b+c14 3 202320238 abcd4 a+b+c=18ma+b+d=18n mn c-d=18m-n 20238r a=18a1+rb=18b1+rc=18c1+r a1b1c1 a+b+c=18a1+b1+c1+3r 18|a+b+c18|3r6|rr=20232023=55×18+202320232023202320238 4 N2023N10 N N572=49a3≥1a4≥2ak a1+1a2+1an+1=10 a3+1≥2a4+1≥310=2×5 a1+1=a2+1=a5+1=…=an+1=1 a1=a2=a5=…an=0N257a4+1≥32 a3+1a4+1=10 a3+1=5a4+1=2a3+1=2a4+1=5N=52-1×75-1=5×74=20235 5 N202320232023000N21 210=2023211=2023202320232023024=210N102 5 6 11 900 xyz2023 x2+y2+z2≤10 1≤x≤30≤y≤30≤z≤3 202320232023202320232 202320232023202320232 202320232023202320230 202301 7 N202352NN2023 N N|100N=20232023 N|2023N=202320232023500 4NN=2023202320232023202320232023 14 1k10k 2 8 2023202320233 13+15+23=2023=3×17 202317 3 20235 2023 179 188 2023 269 278 2023 359 368 377 (11)449 (12)458 (13)467 (14)557 (15)566 3+5+5=133+3+9=155+9+9=23 2023 9 12 202320232023202396 202320232 202320232023202320230 202320232023202326 20232023202312 m+2m+3m+2023m202312 2m为2023312m+2m+3m+4m+202320232 : 13+213+313+13 n=1×2×3×…×n12 m+1+2m+1+3m+1+m+1m 10 2023 1 2 3 4 5 2023 2023202320237 202320233 2023731 20233 20231 20231 20237 20233 20239=4×499+2023202317 11 100 N 1N=2aa=20232a 2N=2a+mm2a2m N=202300=26+362×36=2023 20232023 12 20230 2023 223 1 2 2023-1=2 33 20233+1 55 9-3+1=5 2023+3+9=13 14 14+13=27 1+3+9+27=40 133233 13 | 
