Find the only integer between 1500, and 2500 which is ans integral multiple of both 2 to the power of five and 2 to the power of 5 subtract 1.
2^5 = 32
2^5 - 1 = 31
However, 32 x 31 = 992, which is not between 1500 and 2500. Multiplying again by either term gives you a product of over 31,000.
I hate to admit it, but I cannot answer your question. Is there any typo in your message that might validate my answer?
Sorry that I cannot help more. Thanks for asking.
How about 64*31. Your question does not say 2^5 or 32 is the highest power of 2, only that 32 divides the number.
32=2 5
You're right, my previous answer was incorrect. I apologize for the confusion. Let's reconsider the problem.
To find an integer between 1500 and 2500 that is an integral multiple of both 2 to the power of five (32) and 2 to the power of five subtract 1 (31), we can start by considering multiples of 32 and checking if they are also multiples of 31.
Starting with 32, we can find the next multiple of 32 by adding 32 repeatedly until we reach a number greater than 2500.
32 * 1 = 32
32 * 2 = 64
32 * 3 = 96
32 * 4 = 128
...
32 * 49 = 1568
32 * 50 = 1600 (greater than 1500)
However, none of these numbers are divisible by 31. So, let's start again and check the multiples of 31.
31 * 1 = 31
31 * 2 = 62
31 * 3 = 93
31 * 4 = 124
...
31 * 48 = 1488
31 * 49 = 1519 (between 1500 and 2500)
Therefore, the only integer between 1500 and 2500 that is an integral multiple of both 32 and 31 is 1519.
Again, I apologize for the previous incorrect response and thank you for bringing it to my attention.