Given a number with digits of the form If the sum of these digits is equal to a number that is divisible by 3 then the number is divisible by 3. Proof follows Starting with with which must be 0.3,6,9 then is said to be divisible by Read more…
Research Links Google: non transitive dice Wikipedia: Non transitive dice Wikipedia: Miwin's dice Non transitive Grime dice £11.93 Consider the following set of dice. Die A has sides 2, 2, 4, 4, 9, 9. Die B has sides 1, 1, 6, 6, 8, 8. Die C has sides 3, 3, 5, 5, 7, 7. The probability that A rolls a higher number Read more…
We present a solution to round 1 question 5 from the 2019 New Zealand Mathematical Olympiad. This problem involves describing all values of a quartic expression which is a perfect square.
Added 9-30-2024: Why the symmetry at 25? I wondered why the symmetry at N=25. For this you look at This is what you see in the excel table around N=25. Excel File here Walking the beira mar here in Sao Jose, SC. Keeping my mind busy during Read more…
Notes Used extended Euclidean algorithm Uses and demonstrates factor substitution method well
Research Links Google: diophantine equation pythagoras Chapter 1: DIOPHANTINE ANALYSIS – UnKnown Book Diophantine Equations – Chapter 5 – Diophantine Analysis monograph by Robert Daniel Carmichael Pythagorean Triples Solution The square of the odd number is Hence the sum of two odd squares is divisible by 2 but Read more…
A good example of usage of modulus arithmetic.
Research Links Google: problem 6 1988 olympiad PDF: A Solution to 1988 IMO Question 6 Wikipedia: Vieta's formulas PDF: Vieta Jumping Example problems Vieta Root Jumping
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