IOQM Prime Number Question with Solutions PDF

IOQM Prime Number Question section in IOQM 2026 tests students on prime properties, algebraic expansions, digit-based reasoning, and logical deduction. Problems included cube expressions, consecutive primes, sequence analysis, and factorization-based reasoning.

This guide provides structured explanations, key concepts, and preparation strategies based on the IOQM prime number previous year questions. Regular practice of ioqm prime number problems with solutions helps students build strong Number Theory fundamentals and improve accuracy in Olympiad exams.

Also Read: 

• IOQM Previous Year Question Papers
• IOQM Syllabus

IOQM Prime Number Question with Solutions

Below is an example of some IOQM Prime Number Question problems from the chapter Number Theory.

1. Prime p such that 16p + 1 is a Perfect Cube

Let:

16p+1=(2a+1)316p + 1 = (2a+1)^316p+1=(2a+1)3

Expanding:

(2a+1)3=8a3+12a2+6a+1(2a+1)^3 = 8a^3 + 12a^2 + 6a + 1(2a+1)3=8a3+12a2+6a+1

After simplification:

p=4a2+6a+3p = 4a^2 + 6a + 3p=4a2+6a+3

For a=8a = 8a=8:

p=307p = 307p=307 p−300=7p - 300 = 7p−300=7

✔ Final Answer: 7

This IOQM Prime Number Question tested algebraic expansion combined with prime identification.

2. Prime Count in a Special Sequence

How many of the first ten numbers of the sequence 121, 11211, 1112111, … are prime numbers?

General term structure shows:

Each term is composite.

✔ Number of primes in first ten terms: 0

Many ioqm prime number previous year questions involve identifying hidden factorization patterns like this

3. Consecutive Primes Representation

Given expressions represent:

p,2p,q,2qp, 2p, q, 2qp,2p,q,2q

Using sum logic:

p+q=2n−9p + q = 2n - 9p+q=2n−9

Since sum is odd → one prime must be 2.

Thus:

• p=2p = 2p=2
  
  

• q=3q = 3q=3
  
  

• n=7n = 7n=7
  
  

✔ Final Answer: 7

This IOQM Prime Number Question reinforces the uniqueness of the even prime.

IOQM Prime Number Question PDF Download

Looking for the IOQM Prime Number Question PDF Download to strengthen your Number Theory preparation? This PDF includes carefully selected IOQM prime number questions, detailed solutions, and previous year patterns to help you master prime-based Olympiad problems effectively.

Why IOQM Prime Number Question Practice is Important

The IOQM Prime Number Question section:

• Appears consistently in IOQM exams

• Tests deep number theory understanding

• Requires logical speed and clarity

• Rewards strong fundamentals

Practicing IOQM prime number previous year questions helps students identify patterns and common traps.

Preparation Strategy for IOQM Prime Number Question

Consistent practice of IOQM Prime Number Question types ensures improved accuracy and time management.

1. Master prime factorization techniques.

2. Practice algebraic cube and expansion problems.

3. Solve structured IOQM prime number questions daily.

4. Revise previous IOQM sets thoroughly.

5. Focus on elimination-based reasoning.
   
   

Mastering the IOQM Prime Number Question requires strong conceptual clarity, consistent practice, and analysis of previous year trends. With structured preparation and regular revision, students can confidently tackle even the most challenging prime-based problems in IOQM.

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