# 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

## 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

## (10*a + b) * c = a^2 + b^2 + c^2

Paul found – Part 1   Pattern #2 :

Posted in Uncategorized | Tagged , , | 2 Comments

## 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

Posted in Number Puzzles | Tagged , | 1 Comment

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

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

Posted in Number Puzzles | Tagged , | 5 Comments

## 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

Posted in Number Puzzles | Tagged , , | 5 Comments

## (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

## product of tangents

the pattern continues.     Can you explain why?