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Ask iit jee aieee pet cbse icse state board community Community Discussion Question: No. of solutions
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mathiit (0)

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Find the number of positive solutions for the equation 3x+5y=1008

    
rudra.panda (2514)

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Is the answer 67? If yes i will post the solution.

God does not care about our mathematical difficulties. He integrates empirically. ~~~Albert Einstein (1879-1955)~~~~
To divide a cube into two other cubes, a fourth power or in general any power whatever into two powers of the same denomination above the second is impossible, and I have assuredly found an admirable proof of this, but the margin is too narrow to contain it.~~~Pierre de Fermat (1601-1665)~~~

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rudra.panda (2514)

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Please correct if wrong...........


 


Let\ x,y\ belogs\ to N\ such\ that\ 3x+5y=1008\\\\Then\ 3|5y\ or\ 3|y\\\\\Rightarrow y=3k\\\\Now,\ 3x+15k=1008\\\\\Rightarrow x+5k=336\\\\\Rightarrow 5k\le335\\\\\Rightarrow k\le67\\\\\text{Thus, any solution pair is given by (x,y)=(336-5k,3k) where}\ 1\le k \le 67.\\\\\text{ So number of positive solutions is 67.}\\\\\\\\\text{Correct if i am wrong.}


God does not care about our mathematical difficulties. He integrates empirically. ~~~Albert Einstein (1879-1955)~~~~
To divide a cube into two other cubes, a fourth power or in general any power whatever into two powers of the same denomination above the second is impossible, and I have assuredly found an admirable proof of this, but the margin is too narrow to contain it.~~~Pierre de Fermat (1601-1665)~~~

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RyuAmakusa (680)

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i think u ment integeral sol. right. u can see that the x intersecpt is 336. both x and y should be int. now 3x should end with 3 or 8 so x can be 1,6,11,..... u can apply A.P formula 1+(n-1)5=336 => n=68 this also includes (336,0) that we do not want so 67
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mathiit (0)

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Sorry that is no. of integral solutions.
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