It’s midnight already. I’m going to bed after I type this. Now the fourth Euler problem: A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 99. Find … Continue reading → [Read more...]

The third problem: The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number 600851475143 ? My solvement is straightforward: firstly to identify all the prime numbers between 2 and sqrt(n); secondly … Continue reading → [Read more...]

Almost my time for bed. Just write a quick solution on the second problem of Project Euler. Here it is. Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, … Continue reading → [Read more...]

Things have been going wild since I opened this blog. Tasks were piled up while I was tight on time. At present, I’m facing a major challenge in my life. However, I decide to spare some time for self-improvements. R … Continue reading → [Read more...]

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It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square. 9 = 7 + 212 15 = 7 + 222 Read More: 461 Words Totally [Read more...]

Starting with 1 and spiralling anticlockwise in the following way, a square spiral with side length 7 is formed. 37 36 35 34 33 32 31 38 17 16 15 14 13 30 Read More: 597 Words Totally [Read more...]

It is possible to show that the square root of two can be expressed as an infinite continued fraction. √ 2 = 1 + 1/(2 + 1/(2 + 1/(2 + … ))) = 1.414213… By expanding this for the first four iterations, we get: Read More: 547 Words Totally [Read more...]

http://projecteuler.net/index.php?section=problems&id=187 A composite is a number containing at least two prime factors. For example, 15 = 3 × 5; 9 = 3 × 3; 12 = 2 × 2 × 3. There are ten composites below thirty containing precisely two, not necessarily distinct, prime factors: 4, 6, 9, 10, 14, 15, 21, 22, 25, 26. Read More: 671 Words Totally [Read more...]