Tag Archives: Sums

When x ± y, x ± z, y ± z are squares

    Find positive integers     so that the expressions are to made squares.   Here are some solutions:   ,      ,        ,      ,        ,     ,     ,     ,     , … Continue reading

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4 + 5 + 6 + … + m = (m+1) + (m+2) + … + n — (Part 4)

      Here are the first few solutions:                                      

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3 + 4 + 5 +…+ m = (m+1) + (m+2) +…+ n — (Part 3)

                                                   

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2 + 3 +…+ m = (m+1) + (m+2) +…+ n —- (Part 2)

    Here are the first few examples:                                            

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1 + 2 + 3 +…+ m = (m+1) + (m+2) +…+ n

    Find all pairs in positive integers     such that   For example,                                          

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Pos+ integers (a,b); a + (a+1) + (a+2) + … + (b-1) + b = a*b

    Pairs     of positive integers for which     3 + 4 + 5 + 6 = 18 =   15 + 16 + 17 + … + 34 + 35 = 525 =   85 + … Continue reading

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Use digits 1, 9, 9, 8 to make numbers from 1 to 100

  Use digits   1, 9, 9, 8   and the basic operations to make numbers from 1 to 100. You may also use decimal points.   Here are, for example, the numbers from   1   to   10 … Continue reading

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Using digits 9,9,9,9 make numbers from 1 to 100

  Use digits   9, 9, 9, 9   and the basic operations to make numbers from 1 to 100. You may also use decimal points.   Here are the numbers   1   to   14 :     … Continue reading

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Sets of positive integers whose sum equals their product

        Find more solutions.                                

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Concatenation| Sum of consecutive integers in descending order (Part 2)

  Part 1:   Concatenation| Sum of consecutive integers: a+b+…+n = a||n   19   +   18   +   17   +   …   +   2   +   1   +   0   = … Continue reading

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