How many pairs of positive integers m,n satisfy the eqn 1/m+4/n=1/12 where n is an odd integer less than 60?
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Concept behind questions where we have to find integer solutions is to just express one variable in terms of other. Here, I wrote M in terms of N. Why? Both the numbers are positive, thus denominator will be more than 0. Had I written N in terms of M, meaning M in denominator, I would have only got the lower bound. Thus, M could have any value for upper bound. But, N had a constraint of having an upper bound less than 60, thus putting N in denominator gave me its lower bound, thus giving me its complete range. Furthermore, since N can only be odd, it was easy to find possible values using the range.
Academic discussion and doubt solving for: HCF & LCM, Integral Solutions, Divisibility Rules, Factorisation, Unit Digit, Remainders.
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