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PKJD-009 ### Step 1: Understanding the Problem The first step is to grasp what the problem is asking. Here, the problem is to compute the value of ( A imes B ) modulo ( N ). This means I need to multiply numbers together and then find the remainder when that product is divided by another number. ### Step 2: Breaking Down the Problem To solve this, I can break it down into smaller, more manageable parts: 1. **Multiplication**: ( A imes B ) is the start. 2. **Modulo Operation**: ( mod N ) involves dividing the previous result by ( N ) and finding the remainder. ### Step 3: Multiplication First, I'll tackle the multiplication part. Let's say ( A = 123 ) and ( B = 456 ). Multiplying these two numbers: - ( 123 imes 456 = ) ? To make this easier, I'll use the standard algorithm of multiplication: 1. Multiply ( 123 ) by ( 460 ). 2. Multiply ( 123 ) by ( -4 ). 3. Add both results to find the product. Wait, this seems off. Actually, it's better to multiply ( 123 ) by ( 456 ) directly: - ( 123 imes 456 = 123 imes (400 + 50 + 6) = 123 imes 400 + 123 imes 50 + 123 imes 6 ) Calculating each part: - ( 123 imes 400 = 49,200 ) - ( 123 imes 50 = 6,150 ) - ( 123 imes 6 = 738 ) Adding these up: ( 49,200 + 6,150 + 738 = 56,088 ) So, ( A imes B = 56,088 ) ### Step 4: Modulo Operation Now, I need to find ( 56,088 mod N ). Let's say ( N = 1,000 ). So, I need to find the remainder when ( 56,088 ) is divided by ( 1,000 ). This involves dividing ( 56,088 ) by ( 1,000 ) and seeing what's left: - ( 56,088 div 1,000 = 56 ) with a remainder since ( 1,000 imes 56 = 56,000 ) - Remainder: ( 56,088 - 56,000 = 88 ) Thus, ( A imes B mod N = 88 ) ### Step 5: Conclusion After performing the multiplication and the modulo operation, I've found that the final answer is ( 88 ). (ox{88})

2019年11月14日84 分