Natural numbers + the proof - practice problems
Number of problems found: 10
- Odd/even number
Pick any number. If that number is even, divide it by 2. If it's odd, multiply it by three and add one. Now, repeat the process with your new number. If you keep going, you'll eventually end up at one every time. Prove. - Whenever 12151
Mickey got so many candies that all the digits in this number were the same. Prove that whenever he can divide such several candies into 72 equal piles, he can also divide them into 37 equal piles. (Note: candies cannot be broken) - Three numbers
How much do we increase the sum of three numbers when the first enlarges by 14, the second by 15, and the third by 16? Choose any three two-digit numbers and prove the results. - Justification 8468
The natural number n has at least 73 two-digit divisors. Prove that one of them is the number 60. Also, give an example of the number n, which has exactly 73 double-digit divisors, including a proper justification. - Directly 55591
If n is a natural number that gives a division of 2 or 3 when divided by 5, then n gives a residue of 4 when divided by 5. Prove directly - Theorem prove
We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption do we start? - Decreasing 36183
Prove that the sequence {3 - 4. n} from n = 1 to ∞ is decreasing. - Engineer Kažimír
The TV show example beautifully illustrates the difference between politicians-demagogues and reasonable people with at least primary education. Engineer Kažimír says that during their tenure, there was a large decline in the price of natural gas. The pri - Sum of inner angles
Prove that the sum of all inner angles of any convex n-angle equals (n-2).180 degrees. - Five-minute 80951
Karel has an average grade of exactly 1.12 from five-minute episodes. Prove that at least 22 of them have one.
We apologize, but in this category are not a lot of examples.
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