27 Sep '08 18:101 edit

if you(ie.me) don't know number theory , it's not.

here goes, is there an algebraic proof, so to speak, for this property?

56 + 9 = 65

I've figured out this much, but its not generalized.

10a + b + 9 = 10b + a...........where b = (a+1)

10a + (a+1) + 9

10a + a + 10

10(a+1) + a

10b + a = 10b + a

there is also the reverse where 10a + b -9 = 10b + a, if b = (a-1).

but how is it proven for any number of consecutive digits, when the number added or subtracted = 9*10^(k-2), where = k the number of digits

here goes, is there an algebraic proof, so to speak, for this property?

56 + 9 = 65

I've figured out this much, but its not generalized.

10a + b + 9 = 10b + a...........where b = (a+1)

10a + (a+1) + 9

10a + a + 10

10(a+1) + a

10b + a = 10b + a

there is also the reverse where 10a + b -9 = 10b + a, if b = (a-1).

but how is it proven for any number of consecutive digits, when the number added or subtracted = 9*10^(k-2), where = k the number of digits