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Foggo did n't tell the purchasing officer about his personal ties to Combs or Wilkes , a government official says . " Just at the moment there are rather a lot of ( cases ) ... Is it always true that either three red numbers or three blue numbers will form an arithmetic progression ? Ramsey theory goes further by proving the existence of highly regular mathematical patterns among sets of integers and other mathematical objects . Instead of focusing on what happens in an equilateral triangle with all three dogs moving at the same speed , he looked at a more general case involving triangles that are not equilateral .