Talk:Discrete Maths for Olympiads

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A Number Trick[edit]

Let us consider a very famous number trick-
Step1:Choose a 3-digit positive integer, where hundred's digit is greater than one's digit.
Step2:Reverse [step1] and subtract from itself.
Step3:Considering [step2] as 3-digit, reverse it and add to itself.
Prediction- Output is always 1089
Justify

A question from RMO[edit]

Prove that if

  • integers a,b,c : a < b < c
  • gcd(c-a,c-b)=1
  • for an integer d: a+d,b+d,c+d form sides of a right angle triangle

Then

  • c+d=l2+m2for some int m,n