Let R1 and R2 respectively denote the maximum and minimum possible remainders when (276)n is divided by 91 for any natural number n,n>= 144. Find R1+R2.  Pick one:
A) 89
B) 90
C) 91
D) 92
E) 93
But the least value for n can be= 144 (as given in question, n&gt;=144)   So, 3n/91= 3*144/91= 68   now, the highest remainder can be when it reaches  68+3+3+3+3+3+3+3= 
<gadget id="calculator"> 68+3+3+3+3+3+3+3</gadget>
<output>89</output>
89   (as each time we increment n by 1 the remainder increases by 3,   3*145/91= 71- remiander   3*146/91= 74   3*147/91=77   ... so on and so far upto 89 after which it becomes 89+3= 
<gadget id="calculator">89+3</gadget>
<output>92</output>
92 which means it crosses 91)   Hence least remainder would be  92 -91= 
<gadget id="calculator"> 92 -91</gadget>
<output>1</output>
1   and highest remainder= 89   R1+ R2= 89+1= 
<gadget id="calculator">89+1</gadget>
<output>90</output>
90   ANSWER:90
<result>B</result>
Let R1 and R2 respectively denote the maximum and minimum possible remainders when (276)n is divided by 91 for any natural number n,n>= 144. Find R1+R2.