Show that the cube of any positive integer 2m or 2m + 1
tusharmodi47:
8m³
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let a be any positive integer and q be the question and answer the r reminder .
according to Euclid division algorithm
possible remainder =0,1
a=bq+r
a=2b+0
cube=
acube=2bcube
acube=8
ontaking 2 common
acube=2(4d)
let 4b be m
acube=2m
similarly,
acube=2b+1
acube=2b+1cube
acube=8bcube+1cube+3×8b×1
acube=8bcube+24b+1
taking 2 common
acube=2(4b+8b)+1
let 4b+8b=m
so,
acube=2×m+1
acube=2m+1
according to Euclid division algorithm
possible remainder =0,1
a=bq+r
a=2b+0
cube=
acube=2bcube
acube=8
ontaking 2 common
acube=2(4d)
let 4b be m
acube=2m
similarly,
acube=2b+1
acube=2b+1cube
acube=8bcube+1cube+3×8b×1
acube=8bcube+24b+1
taking 2 common
acube=2(4b+8b)+1
let 4b+8b=m
so,
acube=2×m+1
acube=2m+1
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