MyInteger.rb

require "Prime"

class Integer
	def isEven?
		self%2==0
	end
	def isOdd?
		self%2==1
	end

	def isPalindromic? base=10
		self.to_s(base)==self.to_s(base).reverse
	end

	def isFactorOf? anInteger
		anInteger%self==0
	end
	def isPrime?
		(2..Math.sqrt(self).to_i).each {|num| return false if num.isFactorOf? self}
		true
	end
	def multiplicityOf primeFactor
		remainer = self
		exponent = 0
		while primeFactor.isFactorOf? remainer
			remainer /= primeFactor
			exponent += 1
		end
		[exponent, remainer]
	end
	def primeFactorsAndMultiplicities
		factors = []
		selfRemainer = self
		Prime.upto(Math.sqrt(self).to_i) {|num|
			multiplicity, selfRemainer = selfRemainer.multiplicityOf(num)
			factors.push([num, multiplicity]) if multiplicity!=0
		}
		factors.push([selfRemainer, 1]) if selfRemainer!=1
		factors	
	end
	def primeFactors
		factors = []
		primeFactorsAndMultiplicities.each{|factor, multiplicity| factors.push factor}
		factors
	end
	def factorsNumber
		number = 1
		primeFactorsAndMultiplicities.each{|factor, multiplicity| number *= (multiplicity+1)}
		number
	end

	def zeroInDigits
		to_s.each_char {|ch| return true if ch=='0'}
		false
	end
	def hasDigitInDuplicate base=10
		# By default check all, i.e., '0'-'9'
		digitShown = Array.new(base, false)
		to_s.each_char {|ch|
			return nil if ch.to_i>=base
			return true if digitShown[ch.to_i]
			digitShown[ch.to_i] = true
		}
		false
	end
	def hasSameDigitAs num
		digitShown = Array.new(10, false)
		to_s.each_char {|ch| digitShown[ch.to_i] = true}
		num.to_s.each_char {|numCh| return true if digitShown[numCh.to_i]}
		false
	end

	def isLychrelUnderIterations? max
		value = self
		max.times {
			value += value.to_s.reverse.to_i
			return false if value.isPalindromic?
		}
		true
	end
end