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2. Collatz conjecture - Wikipedia

   en.wikipedia.org/wiki/Collatz_conjecture

   For instance, the first counterexample must be odd because f(2n) = n, smaller than 2n; and it must be 3 mod 4 because f 2 (4n + 1) = 3n + 1, smaller than 4n + 1. For each starting value a which is not a counterexample to the Collatz conjecture, there is a k for which such an inequality holds, so checking the Collatz conjecture for one starting ...

3. Parity of zero - Wikipedia

   en.wikipedia.org/wiki/Parity_of_zero

   Half of the numbers in a given range end in 0, 2, 4, 6, 8 and the other half in 1, 3, 5, 7, 9, so it makes sense to include 0 with the other even numbers. However, in 1977, a Paris rationing system led to confusion: on an odd-only day, the police avoided fining drivers whose plates ended in 0, because they did not know whether 0 was even. [ 67 ]

4. Palindromic number - Wikipedia

   en.wikipedia.org/wiki/Palindromic_number

   Palindromic number. A palindromic number (also known as a numeral palindrome or a numeric palindrome) is a number (such as 16461) that remains the same when its digits are reversed. In other words, it has reflectional symmetry across a vertical axis. The term palindromic is derived from palindrome, which refers to a word (such as rotor or ...

5. Amazon's No. 1 best-selling pillows are 20% off: 'It ... - AOL

   www.aol.com/lifestyle/amazons-no-1-best-selling...

   Be sure to select the coupon on the product page to get 20% off your purchase at check out. Amazon. $69 $129 Save $60. This is an outrageous price for AirPods! In fact, it's a record-low price, so ...

6. The 10 best sales this weekend to know about: Target ... - AOL

   www.aol.com/lifestyle/the-10-best-sales-this...

   Volupsa Candle Trio. $30 $36 Save $6. Make your bathroom smell like a spa. Discover citrus and fruity notes from fragrances Goji & Tarocco Orange, and Panjore Lychee, and woody notes from French ...

7. Coach Outlet's massive summer sale is here: Get 70% off new ...

   www.aol.com/lifestyle/coach-outlets-massive...

   Now through July 30 you can get an extra 20% off your purchase at Coach Outlet when you buy two or more leather goods. That's right: Stock up on, say, a leather bag and matching wallet, and you'll ...