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Let colors Red, Green and Blue be assigned to integers {1,2,...,n}. The classical
theorem of Van der Waerden claims that if n is large enough then one can always find an arithmetic
progression in one color. For example 3, 6, 9 all colored in Red.
We investigate the conditions on colorings containing totally multicolored
arithmetic progressions. In particular, this talk will provide an answer to the following
question:
" What colorings of {1, 2, ..., n} in three colors always contain an arithmetic
progression {x, x+d, x+2d} with elements colored in three distinct colors?"
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