Number Theory5 questions

Number Theory — JEE Maths Practice Questions & Solutions

5 questions on Number Theory with full step-by-step solutions, including past-year (PYQ) problems. Free to practice.

1^2, 2^2, 3^2, \ldots, 1999^2

101,\,104,\,109,\,116,\,\ldots

a_n=100+n^2

n=1,2,3,\ldots

n

d_n

a_n

a_{n+1}

k

d_n

n

\dfrac{k-1}{20}

x_1,x_2,x_3,x_4,x_5

x_1+x_2+x_3+x_4+x_5 = n^3 \qquad\text{and}\qquad x_2+x_3+x_4 = m^2 ,

m

n

\dfrac{n^3+m^2}2

f

f(n)=\begin{cases}n-3, & \text{if } n\ge1000,\\[2pt] f(n+5), & \text{if } n<1000.\end{cases}

f(84)

N=2222^{5555}+5555^{2222}

r

N

462

r

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