squeak
brute force method using Excel: (only copy and paste what is between the quotation marks)
Cell A1 “1”, Cell B1 “=((((((A1)*5/4+1)*5/4+1)*5/4+1)*5/4+1)*5/4+1)”, Cell C1 “=B1-INT(B1)”
Select Cells A1 – A3 and move the cursor to the bottom right hand corner of Cell C1 until it turns into a + sign. Now click on the + sign and drag the formulas down a few thousand rows.
Select column “C” and on the “Standard” toolbar click “Sort Ascending” (The icon has an A on top of a Z with a down arrow on the right side). Select to “Expand the Selection” and click “Sort”. The rows where the entry in column C is 0 are possible solutions.