What numbers are called co-primes?
First you need to know what prime numbers are:prime numbers are natural numbers[1] greater than [math]1[/math] that have only two divisors that don’t leave a reminder: [math]1[/math] and themselves.The first twenty primes are [math]2[/math],[math]3[/math], [math]5[/math], [math]7[/math], [math]11[/math], [math]13[/math], [math]17[/math], [math]19[/math],[math]23[/math], [math]29[/math], [math]31[/math], [math]37[/math], [math]41[/math], [math]43[/math], [math]47[/math], [math]53[/math], [math]59[/math], [math]61[/math], [math]67[/math] and [math]71[/math].There infinite many primes[2] and every natural number greater than [math]1[/math] not a prime can be expressed by a unique prime product[3].Now if two natural numbers are co-prime they have no prime number in their product in common.For example [math]10=2 \times 5[/math] and [math]21=3 \times 7[/math] are co-prime since they don’t have any prime factor in common, where as [math]14=2 \times 7[/math] and [math]18=2 \times 3^2[/math] are not co-prime since the share the prime factor [math]2[/math].Footnotes[1] Natural number - Wikipedia[2] Euclid's theorem - Wikipedia[3] Fundamental theorem of arithmetic - Wikipedia
What is the quantum theory explanation for transparency and opaqueness?
Considering that atoms are mostly empty space, I don't see it as a problem that something as small as a photon could pass easily though matter if it was in the correct configuration. So long as the molecules are spaced sufficiently far apart.
1 4 7 12 19 28 39, what number comes next?
The sequence increases by the next member in the ordered sequence of odd numbers. 7 - 4 = 3, 12 - 7 = 5, 19 - 12 = 7, and so on. So the next number is 39 + 13 = 52.
What are the next numbers in this series: 2.5, 4, 7, 10, 16, 19?
Okay so lets check the series one by one, that is by taking two number at a time.(2.5,4) - the difference is 1.5(4,7) - the difference is 3 or 2×1.5.(7,10)- again the difference is 3.Seems like 3 is repeating. Wait lets investigate further more.(10,16)- the difference is 6 or 2×3.Seems like the pattern difference is 1.5,(2×1.5),(2×1.5),(2×2×1.5).(16,19) - the difference is 3 again.The pattern difference is 1.5,3,3,6,3.So accordingly since 3 is getting repeated two times, the next number in series would likely be 22.Now there are two ways to goFirstly going by recursive method, the pattern difference will be 1.5,3,3,6,3,3,1.5,……so on.By this method the series will be 2.5,4,7,10,16,19,22,23.5…..Secondly going by another method the pattern difference would be 1.5,3,3,6,3,3,12,3,3,24….i.e 1.5,(2×1.5),(2×1.5),(2×2×1.5),(2×1.5),(2×1.5),(2×2×2×1.5),(2×1.5),(2×1.5),(2×2×2×2×1.5)……so on.By this method the series will be 2.5,4,7,10,16,19,22,34,37,40,64…..Edit: This is my first answer in Quora please upvote and share if you really like my answer
What is the next term in the sequence 3, 5, 8, 13, 21?
Actually there can be two answers follwing two different logics :-34 :- by following the normal Fibonacci series.33 :- But if we try to dig it deeper means analyze it thoroughly one more logic is possible.The difference b/w successive digits is increasing gradually in the given series (difference b/w 5 and 3 is 2, 8 and 5 is 3, 8 and 13 is 5, 13 and 21 is 8 and so on ….) now you may say it does not seems to be logical but if you are thinking differently than my assumption that means you are on a right path. Now moving to the next level observe the difference b/w the successive differences (difference b/w 3 and 2 is 1, 5 and 3 is 2, 8 and 5 is 3 and so on….) that’s the natural no. series. Now by following this logic the next no. which is to be added to get next no. in series is 12(12 minus 8 is 4) so adding 12 to 21 will give 33.
What is the next term of this sequence 1, 3, 7, 15, 31, 63, _?
Starting with the first number ‘1’, we move ahead in the way given below:1 x 2 + 1 = 33 x 2 + 1 = 77 x 2 + 1 = 1515 x 2 + 1 = 3131 x 2 + 1 = 6363 x 2 + 1 = 127Therefore 127 is the next number in the series.
What number would come next in the series 7, 9, 13, 21, 37?
The series in this form doesn't make much sense. So it needs to be simplified in a manner which makes it easier to understand….7 , 9 , 13 , 21 , 37We convert this into the (1+x) format……Doing so we get :-(1+6) , (1+8) , (1+12) , (1+20) , (1+36)Now we take the second number in each of the terms….6 , 8 , 12 , 20 , 36Next…we find the difference between each of these terms….2 , 4 , 8 , 16Clearly they are in Geometric Progression with the common ratio of 2…Means after 16, the next term will be (16×2) which is 32…So we add it to the last term of our series….36 + 32 = 68And as we have subtracted one from each term…..we add it back…(68+1) = 69Hence the answer is 69And the series becomes :-7 , 9 , 21 , 37 , 69
What is the next number in the series, 2 3 5 7 11 13 17?
In given series you clearly see that all number is divisible by its own or 1 .This is the definition of prime numbers.Now, i can say that next number in series is 19 ….2 3 5 7 11 13 17 19 23- - - - - so on
Among 5/4, 6/6, 9/6, 4/3, which one is bigger?
Among 5/4, 6/6, 9/6 and 4/3 which one is bigger? The term “bigger” is misleading. Why?The LCM of the denominator is 12. So all the fractions need to be converted to the same denominator. Thus 5/4, 6/6, 9/6 and 4/3 become 15/12, 12/12, 18/12 and 16/12.So 9/6 is the biggest.Why is “bigger” misleading, you ask? Well, 9/6 is bigger than 4/3 which is bigger than 5/4 which is bigger than 6/6. Hence from your question 9/6, 4/3 and 5/4 are bigger than 6/6. Is that what you are looking for?
Does the series converge or diverge, 70 7 .7 .07 .007?
I am confused by what you are saying and what you wrote. {70,7,0.7,0.07, 0.007,....} is a sequence, not a series. If it were a series, then yes, it does converge to 700/9 (geometric series, as the previous answerer proposed). But that is not what you have here. a1 = 7 * 10^1 a2 = 7 * 10^ 0 a3 = 7 * 10^-1 a4 = 7 * 10^-2 . . . an = 7 * 10^(2-n) So lets see lim(n->infinity) 7(10)^(2-n) = 0, so yes, the sequence does converge.