How to Calculate 19⁵-19
=======================
Let us find an easy way to solve it.
Factorizing that expression seems like a good idea:

  19⁵-19 = 19(19⁴-1)
         = 19(19²-1)(19²+1)
	 = 19(19+1)(19-1)(19²+1)
	 = 19✕20(19-1)(19²+1)
	 = 10✕38(19-1)(19²+1)
	 = 10(40-2)(19-1)(19²+1)
	 = 10(40-2)(19-1)[(20-1)²+1]
	 = 10(40-2)(19-1)(20²-2✕20+1²+1)
	 = 10(40-2)(19-1)[20(20-2)+2]
         = 10(40-2)✕18[20(20-2)+2]
	 = 10(40-2)✕[360(20-2)+36]
	 = 10(40-2)✕[360(20-2)+35+1]
	 = 10{(40-2)[360(20-2)+35]+38}
	 = 10{(40-2)[360(20-2)+35]+30+8}
	 = 10{(40-2)[360(20-2)+35]+30}+80
	 = 10{(20-1)[720(20-2)+70]+30}+80
	 = 100{(20-1)[72(20-2)+7]+3}+80
	 = 100{(20-1)[72(20-2)]+7(20-1)+3}+80
         = 100[(20-1)(1440-144)+7(20-1)+3]+80
	 = 100[(20-1)(1440-144)+140-7+3]+80
	 = 100(20✕1440-20✕144-1440+144+140-4)+80
	 = 100(20✕1440-20✕144-1440+280)+80
	 = 1000(20✕144-2✕144-144+28)+80
	 = 1000[(20-2-1)✕144+28]+80
	 = 1000(17✕144+28]+80
	 = 1000(17✕140+17✕4+28)+80
	 = 1000(17✕140+68+28)+80
	 = 1000(17✕140+96)+80
	 = 1000(17✕140+90+6)+80
	 = 1000(17✕140+90)+6080
	 = 10000(17✕14+9)+6080
	 = 10000(170+17✕4+9)+6080
	 = 10000(170+68+9)+6080
	 = 10000(170+70+7)+6080
	 = 10000(170+70)+76080
	 = 10000✕240+76080
	 = 2476080