I guess the difficulty is not in understanding the proof but in coming up with it.
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Funny thing is, right now in Romania this problem can be solved by an slightly above average pupil that is in 6th grade, meaning 13 years old
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I lost it at dividing the difference. Can you explain?
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If x and y are both divisible by z, then (x-y) is too (factoring). So him showing the difference is 1 means no other common factor — disproving the assumption that they have k as common divisor
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Using Principle of Mathematical Induction? Prove for k, k+1
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Who knew? One factorial!
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@Jay_Desai10@themehtaphysics Would've never occured in a million years.
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in general : a*n + b divided by c*n + d is irreductible if d*lcd(a, c)/c - b*lcd(a, c)/a = +- 1
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I by mistake solved this problem for (21n+1)/(14n+3). The proof also kind of works, but the resulting difference is 7 (instead of 1). So the common divisor could be 7, but both 21n+1 and 14n+3 are not divisible by 7.
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