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Why is kg m³ to g cm³1 to 1000? - Mathematics Stack Exchange I understand that changing the divisor multiplies the result by that, but why doesn't changing the numerator cancel that out? I found out somewhere else since posting, is there a way to delete this?
elementary number theory - $2017^ {2016^ {2015}} \mod 1000 . . . I'm trying to solve the following exercise: $$2017^ {2016^ {2015}} \mod 1000,$$ here's what I've already come up with: Using Euler's conrgruence, one finds that $$2017^ {2016^ {2015}} \equiv 2017^ {2016^ {
Exactly $1000$ perfect squares between two consecutive cubes Therefore there are exactly $1000$ squares between the successive cubes $ (667^2)^3$ and $ (667^2+1)^3$, or between $444889^3$ and $444890^3$ Finally, we can verify all of this by using the command line utility bc: $ bc sqrt((667^2)^3) 296740963 sqrt((667^2+1)^3-1) 296741963 Cite edited Nov 27 at 22:11 community wiki 5 revs R P A reflection
algebra precalculus - Multiple-choice: sum of primes below $1000 . . . For example, the sum of all numbers less than 1000 1000 is about 500, 000 500, 000 So, 168 1000 × 500, 000 168 1000 × 500, 000 or 84, 000 84, 000 should be in the right ballpark 76127 76127 is the right answer, by this reasoning
How many numbers between 1 and 1000 are divisible by 2, 3, 5 or 7? The of 210 210 - the number of values between 1 1 and 210 210 that are relatively prime to 210 210 - is (2 − 1)(3 − 1)(5 − 1)(7 − 1) = 48 (2 1) (3 1) (5 1) (7 1) = 48 Using this, we can say that there are 48 ⋅ 5 = 240 48 5 = 240 numbers not divisible by these four numbers up to 1050 1050 Some of these of course are out of range of the original question; we'll have to figure out
What is $\\underbrace{555\\cdots555}_{1000\\ \\text{times}} \\ \\text . . . From here, we can conclude that 555 ⋯ 555 1000 times mod 7 = 4 555 555 ⏟ 1000 times mod 7 = 4 However, I wasn't allowed to use a calculator and solved this in about 12 minutes Another problem was that there was a time limit of about 5 minutes My question is: Is there an easier and faster way to solve this? Thanks a lot in advance!