can you prove this ? "(45 - 45) =45"?Any ideas...?

consider the number 987654321 the sum of the digits is 45.
consider the number 123456789 the sum of the digits is 45.
now subtract 123456789 from 987654321 you get 864197532 the sum of the digits is 45.
Hence 45 - 45 = 45.

I am afraid you cant divide by a-b since you will be dividing by 0 ...

This is true if you use modulo 45 arithmetic
you get
(45 - 45) = 0 = 45

also if you use modulo 3, 5, 9 or 15 arithmetic

.,.,.,..

it cant be unless you take different values for 4 and 5

Unless you redefine either '4' or '5' to be equal to 0, this equation will never be true.

this is not true

Let a = b = 45

Solution:
a = b (then multiply the equation by a)
a^2 = ab (then subtract it by b^2)
a^2 - b^2 = ab - b^2 (then simplify)
(a-b)(a+b) = b(a-b)
a+b = b
a=b-b (then substitute values)
45=45-45

hehe

Let a and b be any equal non-zero quantities.

Then

a = b

Multiplying throughout by a gives

a^2 = ab

Subtract b^2

a^2 - b^2 = ab - b^2

Factorising gives

(a - b)(a + b) = b(a - b)

Dividing throughout by (a - b) gives

a + b = b

Observing that a = b gives

2b = b

So

b = (b - b)

Putting b = 45 gives you your answer.

QED ; )