Give an example of 11 consecutive positive integers the sum of whose squares is a perfect square. Because we respect your right to privacy, you can choose not to allow some types of cookies. Click on the different category headings to find out more and change our default settings.
Suppose first that the number n is a prime number. n = 2 can clearly not be written as the sum of consecutive positive integers, because the first two positive integers are 1 and 2. And all prime numbers other than 2 are odd, and any odd number of the form 2k+1 (k an integer) is the sum of the two consecutive integers k and k+1.
We now want to find out the sum of all these n! numbers are added together. Let us take an example and understand how it is to be done and then look it as a formul. To find the sum of all the four digit numbers formed using the digits 2,3,4 and 5 without repetition: We can form a total of 4! or 24 numbers.
Question 304253: the sum of the squares of two consecutive integers is 365. what are the integers. thx. Answer by JBarnum(2146) (Show Source): You can put this solution on YOUR website! 2*2*2*7*13=728. 7*4=28 13*2=26 so -13 and +28 are the factoring numbers. (-14,-13)or(13,14)
The only two-digit prime whose square is the sum of the squares of two consecutive two-digit numbers: (20^2+21^2). The prime p for which the harmonic series of odd primes (1/3 + 1/5 + 1/7 + 1/11 + ... + 1/p) first exceeds unity. The maximal number of regions into which a circle can be divided by 7 lines.
Let first positive integer be xSo, other positive integer = x + 1According to question,x2 + (x + 1)2 = 365 x2 + x2 + 1 + 2x = 365⇒ 2x2 + 2x – 364 = 0⇒ x2 + x – 182 = 0⇒ x2 + 14x – 13x – 182 = 0⇒ x(x + 14) – 13(x + 14) = 0⇒ (x – 13) (x + 14) = 0⇒ x – 13 = 0or x + 14 = 0⇒ x = 13or x = –14Here x = – 14 does not exist.Therefore, required positive integers are : x = 13 and x + 1 = 13 + 1 = 14.
High-Resolution Geologic Mapping in the Eastern Manus Basin. NASA Astrophysics Data System (ADS) Thal, J.; Bach, W.; Tivey, M.; Yoerger, D. R. 2011-12-01. AUV-based microbathymetry combined with ROV video data was used to create the first high-resolution geologic maps of two hydrothermal active areas in the eastern Manus Basin: North Su volcano and PACManus hydrothermal field on Pual Ridge.
(a) Find all values of X that are mutually beneficial for Dan and firm N, provide graphical solution. (b) Suppose that X=20. A corrupted manager from bank M possesses information about the bank's position and can say with certainty whether bankruptcy will take place. He offers Dan to sell this...
Sum 41 is a video-obsessed pop punk band from Canada. The most frequent sum of digits (known) is 41. The Sun's wobble speed is about 41 feet per second. The smallest prime whose cube can be written as sum of three cubes in two ways (41 3 = 40 3 + 17 3 + 2 3 = 33 3 + 32 3 + 6 3). 41 is the smallest prime beginning with a composite digit.