Tag Archives: Product

When the product of two positive integers is even

    Prove that the product of the positive integers a and b is even if and only if there exist positive integers c and d such that                                                                        … Continue reading

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Products | (x + r_1)(y + r_2) = xy; (r_1, r_2) are rational

    Example #1 :    ,    Integer solutions:    ,    ……………………………………………….. Example #2 :    ,    Integer solutions:    ,    ………………………………………………..   Integer solutions:    ,    ………………………………………………..   there are infinitely many possibilities.   … Continue reading

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(10*a + b) * c = a^2 + b^2 + c^2

      Paul found – Part 1   Pattern #2 :                    

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Puzzle | 4 items in a store; a*b*c*d = a+b+c+d

  PART 1   The price tags on three items in a store are : We note that Find four prices,   a,   b,   c,   and   d   such that   Paul and David answered correctly … Continue reading

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Products (A = B*C) – digits w/o repetition

  Products without repetition of four, five, … ten consecutive digits     Find more examples.                                    

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Product – Min and Max

    The integers   A, B, C, D, E   together contain digits   (1, 3, 5, 7, 9)   exactly twice. [A, B, C, D, E   do not contain any even digits] Find min/max of   A … Continue reading

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(n, n+1) Higher Sum and Product

  Among the distinct pairs of numbers whose sum is   ,   the greatest possible product is   Consider   ,   find the distinct ways of achieving a higher product with two positive integers   Here are the … Continue reading

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product of tangents

    the pattern continues.     Can you explain why?                        

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Smallest integer that can be expressed as product of a number and its reversed

    The smallest number not divisible by 10 expressible for the first three numbers: in 3 ways is   1115892288 : 1115892288   =   13248   *   84231 1115892288   =   23184   *   48132 … Continue reading

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Products| (1+2)(3+4+…+n) is a square, n ≤ 100

      Find all   n ≤ 100   so that (1 + 2 + 3 + 4)(5 + 6 + … + n) (1 + 2 + 3 + 4 + 5)(6 + 7 + … + n) … Continue reading

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