x, y, and z, are consecutive terms of an arithmetic progression,

For **n = 27**, the equation , has exactly two solutions.

And the equation , has exactly three solutions, for n = … 68 more words

x, y, and z, are consecutive terms of an arithmetic progression,

For **n = 27**, the equation , has exactly two solutions.

And the equation , has exactly three solutions, for n = … 68 more words

This is a problem I created in . I proposed it to be used here as problem . Though initially I was a bit careless with the bounds, but just to be safe, I am proving the weak bound here. 367 more words

Find positive integers that can be expressed as the product of three distinct positive integers in A.P. in two ways.

That is,

For example, in one way: … 73 more words

If , then

**c. d.** is the common difference

c. d. =

c. d. =

c. d. =

c. d. =

c. d. =

c. d. 37 more words